Remark 3.7 In the case of \(N=2\) , the determinantal identities above become bilinear equations
satisfied by the tau functions. On the other hand, in the previous work [1]},
we gave conjectural bilinear equations of the tau functions for \(N=2\)  and \(m=1\) .
They are not equal to, and it is not clear whether the bilinear equations obtained in this paper
recover the conjectural bilinear equations (equations (3.16)–(3.23) in [1]}).
